{
  "id": "1712.04027",
  "version": "v1",
  "published": "2017-12-11T21:08:26.000Z",
  "updated": "2017-12-11T21:08:26.000Z",
  "title": "Linear Equations in Singular Moduli",
  "authors": [
    "Yuri Bilu",
    "Lars Kühne"
  ],
  "comment": "17 pages, submitted",
  "categories": [
    "math.NT"
  ],
  "abstract": "We establish an effective version of the Andr\\'e-Oort conjecture for linear subspaces of $Y(1)^n_{\\mathbb{C}} \\approx \\mathbb{A}_{\\mathbb{C}}^n$. Apart from the trivial examples provided by weakly special subvarieties, this yields the first algebraic subvarieties in a Shimura variety of dimension $> 1$ whose CM-points can be (theoretically) determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-11T21:08:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "11G50",
      "14G35",
      "11R37"
    ],
    "keywords": [
      "linear equations",
      "singular moduli",
      "first algebraic subvarieties",
      "trivial examples",
      "shimura variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}